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Maxwell's equations may be combined to demonstrate how fluctuations in electromagnetic fields (waves) propagate at a constant speed in vacuum, c (299 792 458 m/s [2]). Known as electromagnetic radiation , these waves occur at various wavelengths to produce a spectrum of radiation from radio waves to gamma rays .
The maxwell is a non-SI unit. [8] 1 maxwell = 1 gauss × 2. That is, one maxwell is the total flux across a surface of one square centimetre perpendicular to a magnetic field of strength one gauss. The weber is the related SI unit of magnetic flux, which was defined in 1946. [9] 1 maxwell ≘ 10 −4 tesla × (10 −2 metre) 2 = 10 −8 weber
Symbol Name Meaning SI unit of measure alpha: alpha particle: angular acceleration: radian per second squared (rad/s 2) fine-structure constant: unitless beta: velocity in terms of the speed of light c: unitless beta particle: gamma: Lorentz factor: unitless photon: gamma ray: shear strain: radian
In free space, where ε = ε 0 and μ = μ 0 are constant everywhere, Maxwell's equations simplify considerably once the language of differential geometry and differential forms is used. The electric and magnetic fields are now jointly described by a 2-form F in a 4-dimensional spacetime manifold.
The magnetic constant μ 0 appears in Maxwell's equations, which describe the properties of electric and magnetic fields and electromagnetic radiation, and relate them to their sources. In particular, it appears in relationship to quantities such as permeability and magnetization density , such as the relationship that defines the magnetic H ...
Continuous charge distribution. The volume charge density ρ is the amount of charge per unit volume (cube), surface charge density σ is amount per unit surface area (circle) with outward unit normal n̂, d is the dipole moment between two point charges, the volume density of these is the polarization density P.
This theory stipulated that all the laws of physics should take the same form in all coordinate systems – this led to the introduction of tensors. The tensor formalism also leads to a mathematically simpler presentation of physical laws. The inhomogeneous Maxwell equation leads to the continuity equation:
The Maxwell stress tensor (named after James Clerk Maxwell) is a symmetric second-order tensor in three dimensions that is used in classical electromagnetism to represent the interaction between electromagnetic forces and mechanical momentum.